Has anyone used this site or something similar to book a hotel? Does everything go smoothly, no issues? Any places to recommend?

I’ve used it in multiple cities and never had a single problem.

on one instance in manhattan i think they overbooked and we got moved to another branch hotel. Manager had to be involved to get the room. Other times it was fine. Just be careful on peak dates this could be an issue

In general, it can be a wonderful asset, but I've found in NY it isn't great and don't use it here. It's mostly 3 star hotels (I only stay at 4 or higher) and even with them, most, if not all, require a keycard for the elevator.

I have used it a number of times here on LI, and it is terrific.  It is great for daytime meetings without the cost of reserving a room the day before. There are a few good hotels to choose from. While not 5 star, the ones I have used are clean and there is only one that needs a key card.
I have not used it in Manhattan, and as Madison said, you may get some 3 star type hotels, so look for their reviews.